Denny Stepic here! Just going to recap what we learned last class + one more thing.

Solving Exponential Equations

1. Make the bases on each side equal
2. Cancel same bases
3. Solve the remaining exponent equations.

Ex: 2^x = 32
   
      2^x =  2⁵
   
       x  = 5

Exponent Rules:

Logarithmic Functions 

Find the inverse of  f(x) = a^x using this four step method:

1. Replace f(x) with y
2. Reverse the roles of x and y
3. Solve for y in terms of x
4. Replace y with  f ^-1(x)

Ex: Find the inverse of  y = 3x + 2

x = 3y + 2

x - 2 = 3y

y = x - 2 / 3

 f ^-1(x) = x - 2 / 3
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_{Note: If no number is shown beside log we assume it is 10.}

This is called the "seven" rule.

Ex:  log₁₀(1000) = 3
10^3 = 1000 

   **********************  UNRELATED MATH JOKE BELOW **********************